Expression of type ExprTuple

from the theory of proveit.logic.booleans.quantification.existence

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import A, B, Conditional, ExprTuple, Lambda, P, Q
from proveit.logic import Implies, SubsetEq
from proveit.logic.booleans.quantification import general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([P, Q, A, B], Conditional(Implies(general_exists_in_A_Px_st_Qx, general_exists_in_B_Py_st_Qy).with_wrapping_at(2), SubsetEq(A, B))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(P, Q, A, B\right) \mapsto \left\{\begin{array}{c} \begin{array}{l} \left[\exists_{x_{1}, x_{2}, \ldots, x_{n} \in A~|~Q\left(x_{1}, x_{2}, \ldots, x_{n}\right)}~P\left(x_{1}, x_{2}, \ldots, x_{n}\right)\right] \Rightarrow  \\ \left[\exists_{y_{1}, y_{2}, \ldots, y_{n} \in B~|~Q\left(y_{1}, y_{2}, \ldots, y_{n}\right)}~P\left(y_{1}, y_{2}, \ldots, y_{n}\right)\right] \end{array} \end{array} \textrm{ if } A \subseteq B\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	24, 34, 47, 49
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	47, 49
10	Operation	operator: 13 operand: 15
11	Operation	operator: 13 operand: 16
12	ExprTuple	15
13	Literal
14	ExprTuple	16
15	Lambda	parameters: 32 body: 17
16	Lambda	parameters: 35 body: 18
17	Conditional	value: 19 condition: 20
18	Conditional	value: 21 condition: 22
19	Operation	operator: 24 operands: 32
20	Operation	operator: 25 operands: 23
21	Operation	operator: 24 operands: 35
22	Operation	operator: 25 operands: 26
23	ExprTuple	27, 28
24	Variable
25	Literal
26	ExprTuple	29, 30
27	ExprRange	lambda_map: 31 start_index: 45 end_index: 46
28	Operation	operator: 34 operands: 32
29	ExprRange	lambda_map: 33 start_index: 45 end_index: 46
30	Operation	operator: 34 operands: 35
31	Lambda	parameter: 54 body: 36
32	ExprTuple	37
33	Lambda	parameter: 54 body: 38
34	Variable
35	ExprTuple	39
36	Operation	operator: 42 operands: 40
37	ExprRange	lambda_map: 41 start_index: 45 end_index: 46
38	Operation	operator: 42 operands: 43
39	ExprRange	lambda_map: 44 start_index: 45 end_index: 46
40	ExprTuple	48, 47
41	Lambda	parameter: 54 body: 48
42	Literal
43	ExprTuple	50, 49
44	Lambda	parameter: 54 body: 50
45	Literal
46	Variable
47	Variable
48	IndexedVar	variable: 51 index: 54
49	Variable
50	IndexedVar	variable: 52 index: 54
51	Variable
52	Variable
53	ExprTuple	54
54	Variable